8.10.1 problem 15

Internal problem ID [862]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.4, Mechanical Vibrations. Page 337
Problem number : 15
Date solved : Monday, January 27, 2025 at 03:10:28 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} \frac {x^{\prime \prime }}{2}+3 x^{\prime }+4 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 17

dsolve([1/2*diff(x(t),t$2)+3*diff(x(t),t)+4*x(t)=0,x(0) = 2, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = 4 \,{\mathrm e}^{-2 t}-2 \,{\mathrm e}^{-4 t} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 20

DSolve[{1/2*D[x[t],{t,2}]+3*D[x[t],t]+4*x[t]==0,{x[0]==2,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-4 t} \left (4 e^{2 t}-2\right ) \]